Scheil equation

In metallurgy, the Scheil-Gulliver equation (or Scheil equation) describes solute redistribution during solidification of an alloy.

Four key assumptions in Scheil analysis enable determination of phases present in a cast part. These assumptions are:

It should be noted that the fourth condition (straight solidus/liquidus segments) may be relaxed when numerical techniques are used, such as those used in CALPHAD software packages, though these calculations rely on calculated equilibrium phase diagrams. Calculated diagrams may include odd artifacts (i.e. retrograde solubility) that influence Scheil calculations.

The hatched areas in the figure represent the amount of solute in the solid and liquid. Considering that the total amount of solute in the system must be conserved, the areas are set equal as follows:

Since the partition coefficient (related to solute distribution) is

and mass must be conserved

the mass balance may be rewritten as

Using the boundary condition

the following integration may be performed:

Integrating results in the Scheil-Gulliver equation for composition of the liquid during solidification:

or for the composition of the solid:

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